Are there still Gentlemen's clubs in the UK, where women are not allowed, as members?
Yes, White's Club is an example of such a place. There are female dancers and other professionals there but no female members.
One place strictly banning women is Mount Athos, Greece. This ban on women extends also to females of animal species and dates back to a decree banning women entering the Eastern Orthodox monastic peninsula issued by the Byzantine Emperor Constantine Monomachos in 1060. Four Moldovan women trying to sneak into the EU recently tested this ban. News reports say that they were forgiven and not imprisoned.
55 years ago, Times reported how Aliki Diplarakou, Miss Greece of 1929, had dressed up in men's clothes and smuggled herself into the monks' sanctuary on Mount Athos to see with her own eyes what a place without women would be like.
Professions Where Women Are Not Allowed
The priesthood in the Catholic Church is still off-limits for women. The Vatican teaches that women cannot be ordained and has barred further discussion of the issue.
“Women have served in the United States Army since 1775. They nursed the ill and wounded, laundered and mended clothing, and cooked for the troops in camp on campaign; services that did not exist among the uniformed personnel within the Army until the 20th Century.”
“It looks horrible. Do not let women ride bicycles.”
In Malawi, women were not allowed by law to wear trousers from 1965 to 1994, under President Kamuzu Banda's rule.
In Saudi Arabia, the highest religious authorities have issued Fatwas (bans) against women working in 'mixed' environments e.g. shop checkouts. Many employers still defy this ban and the Saudi Labour Ministry has reinstated women fired from their jobs.
Women in Saudi Arabia are not supposed to drive motor vehicles. There is no law against this, but it is a social convention against Saudi women though Beduin women in the desert areas do drive around.